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18,20 O, for which the values of neutron pairing gap ∆ n are largest. This increase of GDR spreading enhances both of its low- and high-energy tails. In the region E γ ≤ 15 MeV, some weak structure of PDR is visible for 18,20 O, and also 22 O (not shown). In the rest of isotopes under study, except for an extension of the GDR tail toward lower-energy, there is no visible structure of the PDR. Fig, 3. Differential EM cross section for 136 Xe (a) and 208 Pb (b). Results obtained using EM cross section of 2 DGDR within PDM (solid lines) and the best fit with χ to the data points (dotted lines) are based on a normalization of GDR (the bump at ∼ 10 MeV) which exhausts 90 % of TRK. Fig. 4. Photoabsorption cross sections obtained within the PDM for some oxygen isotopes. Fig. 5. Electromagnetic cross sections of GDR within PDM for 20,22 O on 208 Pb target. Different lines display results obtained at different projectile energies as indicated in the panels. 77
Since the photon spectral function N ( E γ ) in the EM differential cross section dσ EM/ dE γ (Eq. (17)) is an exponentially decreasing function with increasing E γ , it enhances the low-energy part of the GDR. Therefore, the EM differential cross section dσ EM/ dE γ of GDR can be used as a magnifying glass for the structure of PDR. These cross sections obtained within the PDM are shown in Fig. 5 for 20,22 O. The calculations were carried out for 208 Pb target at various projectile energies as shown in these figures. The PDR shows up in the EM cross sections as a well isolated peak located at around 6 MeV. Varying the projectile energy affects mostly the GDR region (above 10 MeV) of the EM cross section, but not the PDR. 4. Conclusions A review is given on the current status of the study of nuclear resonances. It is demonstrated that the PDM is a simple but yet microscopic model, which is able to describe a variety of resonances under extreme conditions, namely: 1) the GDR at T ≠ 0, including the constant width at T below 1 MeV, the width increase at low T, the width saturation at high T; 2) the EM cross sections for DGDR obtained at near-relativistic energy in 136 Xe and 208 Pb; 3) the possibility of extracting PDR in the EM cross sections of neutron-rich isotopes at low-energy beams. Regarding the GDR at T ≠ 0, it is shown that the mechanism of the width’s increase at 1 ≤ T ≤ 3 MeV and its saturation at T > 3 MeV comes from the coupling of the GDR to non-collective pp and hh configurations at T ≠ 0. Meanwhile this effect is nearly cancelled by the monotonous decrease of the thermal pairing with increasing T at T < 1 MeV. As the result, the GDR width in this low T -region remains nearly temperature independent. This effect is confirmed by calculations in both of the PDM and a macroscopic approach, which takes into account thermal fluctuations of nuclear shapes and pairing field. Concerning the DGDR, the PDM has succeeded to include the effect of anharmonicity between two coupled GDRs. As a result, for the first time, the experimental values of EM cross sections are nicely reproduced by theoretical calculations within the PDM for both 136 Xe and 208 Pb. Finally, the results of calculations within the PDM have demonstrated how the pygmy dipole mode can be depleted due to its coupling to the GDR. This can be the case when the neutron excess cannot be well separated from the stable core. This effect leads to the disappearance of collectivity of the GDR. As a result the photoabsorption cross sections for neutron-rich isotopes have a tail extended toward low-energy region instead of a well-pronounced PDR peak. Nonetheless, since the photon spectral function N ( E γ ) in the EM differential cross is an exponentially decreasing function with increasing E γ , it enhances the low-energy part of the E1-strength distribution, which is insensitive to the variation of beam energy. This feature suggests that a clean PDR peak (without admixture with the GDR) can be seen in the EM cross section (of neutronrich oxygen and calcium isotopes, e.g.) using low-energy, but high-intensity beams at ∼ 50 MeV/n. REFERENCES 1. Harakeh M.N., van der Woude A., Giant resonances - Fundamental high-frequency modes of nuclear excitation. - Oxford: Clarendon Press, 2001. - 638 p. 2. Schmidt R. et al. // Phys. Rev. Lett. - 1993. - Vol. 70. - P. 1767; Boretzky K. et al. // Phys. Lett. - 1996. - Vol. B384. - P. 30; Grünschloβ A. et al. // Phys. Rev. - 1999. - Vol. C60. - P. 051601. 3. Paar N. et al. // Phys. Rev. - 2003. - Vol. 67. - P. 034312; Sarchi D. et al. // Phys. Lett. - 2004. - Vol. B601. - P. 27. 4. Dinh Dang N., Arima A. // Phys. Rev. Lett. - 1998. - Vol. 80. - P. 4145; Nucl. Phys. - 1998. - Vol. A636. - P. 427. 5. Dinh Dang N. et al. // Phys. Rev. - 2001. - Vol. C63. - P. 044302. 6. Moretto L.G. // Phys. Lett. - 1972. - Vol. B40. - P. 1. 7. Dinh Dang N., Zelevinsky V. // Phys. Rev. - 2001. - Vol. C64. - P. 064319; Dinh Dang N., Arima A. // Phys. Rev. - 2003. - Vol. C67. - P. 014304. 8. Pshenichnov I.A. et al. // Phys. Rev. - 1999. - Vol. C60. - P. 044901. 9. Dinh Dang N. et al. // Nucl. Phys. - 2000. Vol. A675. - P. 531. 10. Bortignon P.F. et al. // Nuc. Phys. - 1986. - Vol. A460. - P. 149; Dinh Dang N. // Nucl. Phys. - 1989. - Vol. A504. - P. 143. 11. Kuznesov D. et al. // Phys. Rev. Lett. - 1998. - Vol. 81. - P. 542. 12. Arumugam P., Dinh Dang N. // RIKEN Accel. Prog. Rep. - 2006. - Vol. 39. - P. 28. 78
Page 1 and 2: UDC 539.14 GIANT RESONANCES UNDER E
Page 3 and 4: continuation of the polarization op
Page 5 and 6: The expression for the spectrum N(
Page 7: Fig. 2. Pairing gaps for 120 Sn ave

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